Question: Which of the following numbers is a factor of 75? ${5,6,7,8,12}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $75$ by each of our answer choices. $75 \div 5 = 15$ $75 \div 6 = 12\text{ R }3$ $75 \div 7 = 10\text{ R }5$ $75 \div 8 = 9\text{ R }3$ $75 \div 12 = 6\text{ R }3$ The only answer choice that divides into $75$ with no remainder is $5$ $ 15$ $5$ $75$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $5$ are contained within the prime factors of $75$ $75 = 3\times5\times5 5 = 5$ Therefore the only factor of $75$ out of our choices is $5$. We can say that $75$ is divisible by $5$.